1. Field of the Invention
This invention is concerned with deriving the far-field signature of a marine seismic acoustic source, such as a multi-element air-gun array, from near-field measurements.
2. Description of the Prior Art
As is well known, in the process of marine seismic exploration, a ship-towed submerged acoustic source is periodically triggered to generate an acoustic wave field. The resulting wavefront propagates downwardly into the earth beneath the water, is reflected from sub-bottom earth layers, and returns to the water surface. Near, but below the water surface, arrays of hydrophones, towed by the same or another ship, detect the reflected pressure waves, convert the detected pressure waves to electrical signals and transmit those signals to a signal utilization device.
As is well known, when the acoustic source is triggered, it produces a complex output pressure pulse in the water. Converted to an electrical signal, the output pulse of, for example an air gun, consists of a short wavetrain whose envelope displays an initial fast rise time followed by several rapidly-decaying oscillations. The wavetrain might be, for example, about 200 milliseconds (ms) or less long and is termed the "signature" of the source.
The acoustic wave generated by the source radiates by spherical spreading in all directions such that there is a vertically downgoing direct component as well as an upwardly-travelling component. The water-air interface is an excellent reflecting surface. The upward-travelling component of the acoustic wave is reflected by the water surface and is reversed in polarity to become another vertically downgoing component generally referred to as a ghost.
Marine acoustic sources are usually deployed a few meters beneath the water surface. Assuming a depth of 6 meters and a water velocity of 1500 meters per second (mps), the two-way lag time in the vertical direction between the direct wave and the ghost is 8 ms. Accordingly, the ghost may interfere, with opposite polarity, with the direct wave to further complicate the source signature which circumstance we shall refer to as the ghost effect. Whether we like it or not, the ghost is usually an integral part of the source signature for most all practical purposes.
If the acoustic souce can be considered to be a point source, such as a small explosive charge or a single air gun, the source signature without its ghost is independent of distance (except for spherical spreading) and direction. In practice, a typical acoustic source consists, not of a single element, but of a spatially-distributed array of elements that generate direct arrivals plus the ghost components. That is particularly true of air guns, which are currently fashionable in marine exploration. The spatial dimensions of an array of source elements may be comparable to the wavelengths of the acoustic waves themselves within the useful seismic-frequency pass-band. Therefore, as is well known, the source signature of an array in the near field becomes a function of both distance and direction. The source signature of an array becomes independent of distance (except for attenuation due to spherical spreading) only in the far field. It is the far-field signature that is needed for data processing.
The far field may be firstly defined as the region at a distance from the source array such that the travel time from all the sources of the array is effectively equal. For practical purposes, equality means differences of at most a few (2-5) milliseconds. By this criterion, the far-field distance, for a typical array dimension of 30 or 40 meters, is on the order of 200 meters.
A further criterion defining the far field is related to the ghost component of the source signature. Because of spherical spreading, the relative amplitude of the direct and ghost components vary with distance form the source array. Again, the far-field signature is that distance at which the source signature becomes independent of distance, which for this criterion is that distance at which the ratio of the direct and ghost amplitudes becomes close to that which it would be at very large distances. In practice a 95% development of the ghost component with respect to the direct component would be acceptable. For an array depth of 6 meters, that criterion would give a far-field distance of about 250 meters.
In summary, therefore, close to the source, the level of the direct arrival as seen in the pressure signature will be very much larger than the amplitude level of the ghost. The two amplitude levels become equalized only in the far field.
The main objective of the above discussion is to emphasize that typically, the far-field distance for a marine source array is on the order of 200 to 300 meters. A direct measurement of the far field must therefore be made at that, or a greater, distance directly or nearly directly below the array.
We now address ourselves to the problem of measuring the far-field signature of a multi-element acoustic source array such as an array of air guns.
Most marine seismic exploration projects are conducted over the continental shelf at water depths in the range of less than 25 up to about 200 meters. Thus, a direct measurement of the far-field signature is generally impossible during the course of a normal exploration project. Even if the water depth were greater than 200 meters it would not be practical to tow special receivers at such great depth.
One obvious, time-honored method for measuring the far-field signature of an acoustic array is of course to move into deep water in excess of 200-300 meters. However there are certain problems: Often, deep water may lie a great many miles from the exploration project. The cost of interrupting the seismic survey to make special separate experiments is usually unjustifiable. For another reason, at sea it is nearly impossible to determine the precise relative positions of a source and a receiver that are significantly separated from one another without extremely expensive and elaborate positioning equipment. Hence, far-field measurement of the source array signature in deep water may not be possible nor even useful.
A method for far-field signature measurement from near-field data in shallow water has been proposed by Ziolkowski, et al. in U.S. Pat. Nos. 4,476,550 and 4,476,553 issued Oct. 9, 1984. In that method, the acoustic pressure signature near each gun of an air-gun array is measured in the presence of the pressure signatures of all of the guns. By suitable processing, the far-field signature is derived from the near-field measurements. In the above method, with an array of n guns, the problem is solved iteratively from n separate measurements. In their method, like the deep-water method, Ziolkowski, et al. require precise measurements of the separation between source and receivers as well as a precise measurement of the spacing between elements of the array. As before stated, it is very difficult to accurately measure the position of anything that is towed freely around in the sea.
It is an object of our invention to determine in a simple way, the far-field signature of a marine acoustic source array, during the course of a normal data-acquisition program, in relatively shallow water (e.g. 50 meters or less).